Generalized measures of noncompactness of sets and operators in Banach spaces |
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| Authors: | E Brandani da Silva D L Fernandez |
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| Institution: | 1.Departamento de Matemática – Av,Universidade Estadual de Maringá – UEM,Maringá,Brazil;2.Departamento de Matemática,Universidade Estadual de Maringá – Unicamp,Campinas,Brazil |
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| Abstract: | New measures of noncompactness for bounded sets and linear operators, in the setting of abstract measures and generalized
limits, are constructed. A quantitative version of a classical criterion for compactness of bounded sets in Banach spaces
by R. S. Phillips is provided. Properties of those measures are established and it is shown that they are equivalent to the
classical measures of noncompactness. Applications to summable families of Banach spaces, interpolations of operators and
some consequences are also given. |
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